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**1 - 3**of**3**### doi:10.1155/2010/586312 Research Article Oscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations

"... Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Wewill establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations rtxt − atxτtΔΔΔ ptxγ δt 0 on a ti ..."

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Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Wewill establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations rtxt − atxτtΔΔΔ ptxγ δt 0 on a time scale T, where γ> 0 is a quotient of odd positive integers with r, a, and p real-valued positive rd-continuous functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. Some examples are considered to illustrate the main results. 1.

### ftp ejde.math.txstate.edu (login: ftp) CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS TO NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES

"... Abstract. A classification scheme is given for the eventually positive solu-tions to a class of second order nonlinear dynamic equations, in terms of their asymptotic magnitudes. Also we provide necessary and/or sufficient conditions for the existence of positive solutions. 1. ..."

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Abstract. A classification scheme is given for the eventually positive solu-tions to a class of second order nonlinear dynamic equations, in terms of their asymptotic magnitudes. Also we provide necessary and/or sufficient conditions for the existence of positive solutions. 1.

### Hybrid Systems by Methods of Time Scales Analysis

, 2013

"... The goal of the present paper is to show how to study hybrid systems with complex behavior (including Zeno points) by methods of time scale analysis. We first transform impulsive differential problems with countably many impulses (de-scribing the above hybrid systems) into dynamic problems on a well ..."

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The goal of the present paper is to show how to study hybrid systems with complex behavior (including Zeno points) by methods of time scale analysis. We first transform impulsive differential problems with countably many impulses (de-scribing the above hybrid systems) into dynamic problems on a well chosen time scale domain and then apply a version of Peano’s theorem for multivalued case on time scales in order to achieve an existence result for the considered problem. We thus offer an alternative proof for [22, Theorem 1], where the tools were coming from the theory of measure driven differential inclusions.